SOLUTION: What interest rate would be needed to double an investment in 9 years using continuous compounding? I tried using the equation A=Principal*e^(rate*time)but am not getting anywhere

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: What interest rate would be needed to double an investment in 9 years using continuous compounding? I tried using the equation A=Principal*e^(rate*time)but am not getting anywhere      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 541357: What interest rate would be needed to double an investment in 9 years using continuous compounding?
I tried using the equation A=Principal*e^(rate*time)but am not getting anywhere with it. I would extremely appreciate it if you would include the formula used along with the answer.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A=Principal%2Ae%5E%28rate%2Atime%29
Take natural logarithms on both sides
ln%28A%29=ln%28Principal%29%2Brate%2Atime subtract from both sides ln%28Principal%29
ln%28A%29-ln%28Principal%29=rate%2Atime use properties of natural logaritms
ln%28A%2FPrincipal%29=rate%2Atime
Now we how we can substitute that doubled the investment bit.
ln%282%29=rate%2A9
Your calculator or spreadsheet software can calculate ln%282%29
I calculated rate=ln%282%29%2F9=+0.077016, meaning annual rate=7.7016%
Rounding to 7.7% (or to 7.70%) you end up a few cents short at 9 years, but maybe it's close enough.